\contentsline {paragraph}{The Art of Molecular Dynamics Simulation}{2}
\contentsline {paragraph}{Gromacs manual}{2}
\contentsline {paragraph}{Life - as a matter of fat\nobreakspace {}\cite {mouritsen}}{2}
\contentsline {paragraph}{Membrane force field}{2}
\contentsline {paragraph}{Rigid-body integration}{2}
\contentsline {part}{I\hspace {1em}Running Brahms}{3}
\contentsline {chapter}{\numberline {1}Input parameters}{4}
\contentsline {section}{\numberline {1.1}{\tt brahms.md}}{4}
\contentsline {paragraph}{{\tt deltaT}}{4}
\contentsline {paragraph}{{\tt stepAvg}}{4}
\contentsline {paragraph}{{\tt stepLimit}}{4}
\contentsline {paragraph}{{\tt resetTime}}{4}
\contentsline {paragraph}{{\tt doCheckpoint}}{5}
\contentsline {paragraph}{{\tt stepCheckpoint}}{5}
\contentsline {paragraph}{{\tt stepPdb}}{5}
\contentsline {paragraph}{{\tt runId}}{5}
\contentsline {paragraph}{{\tt applyThermostat}}{5}
\contentsline {paragraph}{{\tt extTemperature}}{5}
\contentsline {paragraph}{{\tt tauT}}{5}
\contentsline {paragraph}{{\tt applyBarostat}}{5}
\contentsline {paragraph}{{\tt extPressure}}{5}
\contentsline {paragraph}{{\tt tauP}}{5}
\contentsline {paragraph}{{\tt flexBox}}{5}
\contentsline {paragraph}{{\tt keepTetragonal}}{5}
\contentsline {paragraph}{{\tt keepSquare}}{5}
\contentsline {paragraph}{{\tt rCutLipLip}}{5}
\contentsline {paragraph}{{\tt rCutWatWat}}{5}
\contentsline {paragraph}{{\tt rCutSolute}}{6}
\contentsline {paragraph}{{\tt rCutSoluteElse}}{6}
\contentsline {paragraph}{{\tt rNebrShell}}{6}
\contentsline {paragraph}{{\tt stepNebr}}{6}
\contentsline {paragraph}{{\tt nebrTabFac}}{6}
\contentsline {paragraph}{{\tt removeSystemTranslation}}{6}
\contentsline {paragraph}{{\tt removeMonolayersTranslation}}{6}
\contentsline {paragraph}{{\tt nSites}}{6}
\contentsline {paragraph}{{\tt nWaters}}{6}
\contentsline {paragraph}{{\tt nDOPCsDSPCs}}{6}
\contentsline {paragraph}{{\tt nDOPEs}}{6}
\contentsline {paragraph}{{\tt nLipids}}{6}
\contentsline {paragraph}{{\tt nSolutes}}{6}
\contentsline {paragraph}{{\tt nTypes}}{6}
\contentsline {paragraph}{{\tt region}}{6}
\contentsline {paragraph}{{\tt adjustRegion}}{6}
\contentsline {paragraph}{{\tt regionAdjusted}}{6}
\contentsline {paragraph}{{\tt randSeed}}{6}
\contentsline {paragraph}{{\tt initHalfCellWat}}{7}
\contentsline {paragraph}{{\tt initUcell}}{7}
\contentsline {paragraph}{{\tt loadStructure}}{7}
\contentsline {paragraph}{{\tt loadVelocities}}{7}
\contentsline {paragraph}{{\tt centerInputStruct}}{7}
\contentsline {paragraph}{{\tt reCenterBilayer}}{7}
\contentsline {paragraph}{{\tt zConstraint}}{7}
\contentsline {paragraph}{{\tt insertSolute}}{7}
\contentsline {section}{\numberline {1.2}{\tt lipid.ff}}{7}
\contentsline {section}{\numberline {1.3}{\tt water.ff}}{7}
\contentsline {section}{\numberline {1.4}{\tt brahms.an}}{7}
\contentsline {subsection}{\numberline {1.4.1}Region dimensions}{7}
\contentsline {paragraph}{{\tt writeAreaVol}}{7}
\contentsline {subsection}{\numberline {1.4.2}Lipid lateral diffusion}{7}
\contentsline {paragraph}{{\tt latDiff}}{7}
\contentsline {paragraph}{{\tt nBuffLatDiff}}{7}
\contentsline {paragraph}{{\tt nValLatDiff}}{7}
\contentsline {paragraph}{{\tt stepLatDiff}}{8}
\contentsline {paragraph}{{\tt limitLatDiffAv}}{8}
\contentsline {paragraph}{{\tt writeLipLatMotion}}{8}
\contentsline {subsection}{\numberline {1.4.3}Transmembrane profiles}{8}
\contentsline {subsubsection}{Electron density profiles}{8}
\contentsline {paragraph}{{\tt edp}}{8}
\contentsline {paragraph}{{\tt sizeHistEdp}}{8}
\contentsline {paragraph}{{\tt stepEdp}}{8}
\contentsline {paragraph}{{\tt limitEdp}}{8}
\contentsline {subsubsection}{Electrostatic potential profiles}{8}
\contentsline {paragraph}{{\tt epp}}{9}
\contentsline {paragraph}{{\tt sizeHistEpp}}{9}
\contentsline {paragraph}{{\tt stepEpp}}{9}
\contentsline {paragraph}{{\tt limitEpp}}{9}
\contentsline {subsubsection}{Lateral pressure profile}{9}
\contentsline {paragraph}{{\tt lpp}}{9}
\contentsline {paragraph}{{\tt sizeHistLpp}}{9}
\contentsline {paragraph}{{\tt stepLpp}}{9}
\contentsline {paragraph}{{\tt limitLpp}}{9}
\contentsline {subsubsection}{Water polarization profile}{9}
\contentsline {paragraph}{{\tt wpp}}{9}
\contentsline {paragraph}{{\tt sizeHistWpp}}{9}
\contentsline {paragraph}{{\tt stepWpp}}{9}
\contentsline {paragraph}{{\tt limitWpp}}{9}
\contentsline {subsection}{\numberline {1.4.4}Radial distribution function in pure water systems}{9}
\contentsline {paragraph}{{\tt rdfWat}}{9}
\contentsline {paragraph}{{\tt rangeWatRdf}}{9}
\contentsline {paragraph}{{\tt sizeHistWatRdf}}{9}
\contentsline {paragraph}{{\tt stepWatRdf}}{9}
\contentsline {paragraph}{{\tt limitWatRdf}}{9}
\contentsline {subsection}{\numberline {1.4.5}Translational self-diffusion and rotational diffusion in pure water systems}{9}
\contentsline {paragraph}{{\tt diffusion}}{9}
\contentsline {paragraph}{{\tt nBuffDiffuse}}{9}
\contentsline {paragraph}{{\tt nValDiffuse}}{10}
\contentsline {paragraph}{{\tt stepDiffuse}}{10}
\contentsline {paragraph}{{\tt limitDiffuseAv}}{10}
\contentsline {chapter}{\numberline {2}Setting up, running and restarting simulations}{11}
\contentsline {section}{\numberline {2.1}System generation}{11}
\contentsline {subsection}{\numberline {2.1.1}Pure water systems}{11}
\contentsline {paragraph}{{\tt initUcell}}{11}
\contentsline {paragraph}{\tt nWaters}{11}
\contentsline {paragraph}{\tt nSites}{11}
\contentsline {subsection}{\numberline {2.1.2}Single-component lipid bilayers}{11}
\contentsline {paragraph}{\tt nLipids}{11}
\contentsline {paragraph}{\tt nWaters}{11}
\contentsline {paragraph}{{\tt initHalfCellWat}}{11}
\contentsline {paragraph}{\tt nSites}{12}
\contentsline {paragraph}{\tt region}{12}
\contentsline {section}{\numberline {2.2}Restarting simulations}{13}
\contentsline {section}{\numberline {2.3}Self-assembly simulations}{13}
\contentsline {subsection}{\numberline {2.3.1}``Disassembling'' run}{13}
\contentsline {subsection}{\numberline {2.3.2}Equilibration run}{13}
\contentsline {subsection}{\numberline {2.3.3}Self-assembly run}{13}
\contentsline {chapter}{\numberline {3}Output}{15}
\contentsline {section}{\numberline {3.1}Screen output}{15}
\contentsline {paragraph}{\tt step}{15}
\contentsline {paragraph}{\tt time/ns}{16}
\contentsline {paragraph}{\tt E/(kJ/mol)}{16}
\contentsline {paragraph}{\tt U/(kJ/mol)}{16}
\contentsline {paragraph}{\tt P/atm}{16}
\contentsline {paragraph}{\tt T\_lip/C}{16}
\contentsline {paragraph}{\tt T\_H2O/C}{16}
\contentsline {paragraph}{\tt A\_lip/(A$^2$)}{16}
\contentsline {paragraph}{\tt V\_lip/(nm$^3$)}{16}
\contentsline {paragraph}{\tt ST/(dyn/cm)}{16}
\contentsline {paragraph}{\tt dipHG/D}{16}
\contentsline {paragraph}{\tt tiltHG/deg}{16}
\contentsline {section}{\numberline {3.2}Output files}{16}
\contentsline {paragraph}{\tt area\_volume.dat}{16}
\contentsline {paragraph}{\tt initialConfiguration.pdb}{16}
\contentsline {paragraph}{\tt inputParameters.log}{16}
\contentsline {paragraph}{\tt simulationSetup.log}{16}
\contentsline {paragraph}{\tt summary.dat}{16}
\contentsline {paragraph}{\tt tailOrderParameters.dat}{16}
\contentsline {paragraph}{\tt topology.log}{16}
\contentsline {paragraph}{\tt trajectory.pdb}{16}
\contentsline {chapter}{\numberline {4}Visualization}{17}
\contentsline {chapter}{\numberline {5}Analysis}{18}
\contentsline {section}{\numberline {5.1}``On-the-fly'' analysis in Brahms}{18}
\contentsline {section}{\numberline {5.2}Post-processing analysis}{18}
\contentsline {chapter}{\numberline {6}Benchmarks}{19}
\contentsline {section}{\numberline {6.1}Single processor}{19}
\contentsline {subsection}{\numberline {6.1.1}Water systems}{19}
\contentsline {subsection}{\numberline {6.1.2}Hydrated lipid bilayers}{19}
\contentsline {part}{II\hspace {1em}Background}{21}
\contentsline {chapter}{\numberline {7}The molecular dynamics methodology}{22}
\contentsline {section}{\numberline {7.1}Foundations}{22}
\contentsline {section}{\numberline {7.2}Interaction potentials}{24}
\contentsline {section}{\numberline {7.3}Rigid bodies}{24}
\contentsline {section}{\numberline {7.4}Forces and torques}{24}
\contentsline {section}{\numberline {7.5}Equations of motion}{25}
\contentsline {paragraph}{Part A}{25}
\contentsline {paragraph}{Part B}{26}
\contentsline {subsection}{\numberline {7.5.1}Integration timestep: how long?}{26}
\contentsline {section}{\numberline {7.6}Periodic boundary conditions}{26}
\contentsline {subsection}{\numberline {7.6.1}Minimum image convention}{27}
\contentsline {section}{\numberline {7.7}Truncation of nonbonded interactions}{27}
\contentsline {section}{\numberline {7.8}Derivation of forces and torques}{27}
\contentsline {subsection}{\numberline {7.8.1}Dipole-dipole interactions: shifted-force variant}{28}
\contentsline {subsubsection}{Dipolar potential}{28}
\contentsline {subsubsection}{Dipolar forces}{28}
\contentsline {subsubsection}{Dipolar torques}{28}
\contentsline {section}{\numberline {7.9}Improving the interaction computations}{28}
\contentsline {subsection}{\numberline {7.9.1}Cell subdivision}{29}
\contentsline {subsection}{\numberline {7.9.2}Neighbour List}{29}
\contentsline {section}{\numberline {7.10}Thermodynamic measurements}{30}
\contentsline {subsection}{\numberline {7.10.1}Potential energy}{30}
\contentsline {subsection}{\numberline {7.10.2}Kinetic energy and temperature}{30}
\contentsline {paragraph}{Mixtures}{30}
\contentsline {subsection}{\numberline {7.10.3}Pressure tensor}{31}
\contentsline {subsubsection}{Virial contribution from nonbonded pair interactions}{31}
\contentsline {subsubsection}{Virial contribution from bonded (Hooke) pair interactions}{31}
\contentsline {subsubsection}{Virial contribution from angle-bending interactions}{32}
\contentsline {subsubsection}{Scalar (hydrostatic) pressure}{32}
\contentsline {subsubsection}{Surface tension}{32}
\contentsline {section}{\numberline {7.11}Temperature control}{32}
\contentsline {subsection}{\numberline {7.11.1}Weak-coupling method - Berendsen thermostat}{32}
\contentsline {section}{\numberline {7.12}Pressure (and temperature) control}{33}
\contentsline {subsection}{\numberline {7.12.1}Box transformation matrix and scaled variables}{33}
\contentsline {subsection}{\numberline {7.12.2}Weak-coupling method - Berendsen barostat}{33}
\contentsline {subsubsection}{Isotropic}{33}
\contentsline {subsubsection}{Anisotropic}{33}
\contentsline {subsection}{\numberline {7.12.3}Stochastic velocity rescaling}{34}
\contentsline {section}{\numberline {7.13}Statistical analysis}{34}
\contentsline {paragraph}{Standard deviation}{34}
\contentsline {chapter}{\numberline {8}Lipids and membranes}{35}
\contentsline {section}{\numberline {8.1}Types of membrane lipids}{35}
\contentsline {section}{\numberline {8.2}Phospholipid structure and self-assembly}{35}
\contentsline {section}{\numberline {8.3}Phospholipid bilayers}{37}
\contentsline {subsection}{\numberline {8.3.1}Structure}{37}
\contentsline {subsubsection}{Structure of the hydrocarbon region: intramolecular order parameters}{38}
\contentsline {subsection}{\numberline {8.3.2}Phase behaviour of lipid bilayers}{38}
\contentsline {subsection}{\numberline {8.3.3}The lateral pressure profile}{38}
\contentsline {subsection}{\numberline {8.3.4}The dipole potential}{41}
\contentsline {subsection}{\numberline {8.3.5}Dynamics}{42}
\contentsline {section}{\numberline {8.4}Summary}{43}
